Question

Draw the graph of the following equations. Also Determine the Coordinates of the vertices of the triangle formed by these lines and the x-axis.

$4x-y-8=0;2x-3y+6=0$

Answer 1

Step 1: Given data:

$$\begin{gathered} 4x-y-8=0............................\left(i\right) \\ 2x-3y+6=0..........................\left(ii\right) \end{gathered}$$

Step 2 : Solving the first equation:

$$\begin{gathered} 4x-y-8=0 \\ \Rightarrow 4x=8+y \\ \Rightarrow x=\frac{8+y}{4}..................................\left(iii\right) \end{gathered}$$

Substituting y values as 0,1,2 We will get the following x-values,

$x$	2	2.25	2.5
$y$	0	1	2

Step 3 : Solving the second equation:

$$\begin{gathered} 2x-3y+6=0 \\ \Rightarrow 2x=-6+3y \\ \Rightarrow x=\frac{3y-6}{2}................................\left(iv\right) \end{gathered}$$

Substituting y values as 0,1,2 We will get the following x-values,

$x$	-3	-1.5	0
$y$	0	1	2

Step 4: Plotting the values of X and Y graphically:

Hence, The coordinates of triangle formed by the lines and x axis are $(-3,0),(2,0),(3,4)$.